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myininaya
 4 years ago
I have the following information:
\[n=p^2q\]
\[k \ge 4\]
\[0<v<n\]
\[0 \le x < pq\]
\[y=\lceil \frac{(vx^k) \mod n}{pq} \rceil \cdot (kx^{k1})^{1} \mod p\]
I want to show:
\[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k1}(ypq)^i \equiv x^k+kypqx^{k1}\]
the congruence is mod n
myininaya
 4 years ago
I have the following information: \[n=p^2q\] \[k \ge 4\] \[0<v<n\] \[0 \le x < pq\] \[y=\lceil \frac{(vx^k) \mod n}{pq} \rceil \cdot (kx^{k1})^{1} \mod p\] I want to show: \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{k1}(ypq)^i \equiv x^k+kypqx^{k1}\] the congruence is mod n

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satellite73
 4 years ago
Best ResponseYou've already chosen the best response.0i can't even read this what class?

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i made a mistake \[\sum_{i=0}^{k}\left(\begin{matrix} k \\ i \end{matrix}\right) x^{ki}(ypq)^i \equiv x^k+kypqx^{k1}\] I'm trying to follow a proof but i don't know how they got from that one part to the other part

satellite73
 4 years ago
Best ResponseYou've already chosen the best response.0yeah well i cannot read what it says. good luck

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.cacr.math.uwaterloo.ca/hac/ its in chapter 11 on page 473 at the bottom

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i wonder if james or zarkon could do it

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0ask me next semester when I've taken cryptography, and I might be able to help you, but right now, I haven't got a clue.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2only the first two values of i will matter (i=0,1) for i>1 you have a \((pq)^2\) part which is \(p^2qq=nq\) which is zero nod n

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i don't see this (pq)^2 part

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0george what kind of math have you had?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2\[{k\choose i}x^{k1}(ypq)^i\] for \(i\ge2\) \[{k\choose i}x^{k1}(ypq)^i={k\choose i}x^{k1}(y^i)(pq)^{i2}p^2qq\] \[=\left({k\choose i}x^{k1}(y^i)(pq)^{i2}q\right)\times n\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0you are so smart to notice the first two values will only matter since n mod n is like totally 0 thanks zarkon

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0I've only had a year and a half of college level math so far, so that means, calc 13, lin. algebra, abstract algebra, and analysis

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0is there any number theory in abstract algebra i can't remember

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0not very much. I'm taking intro to number theory, and cryptography next semester.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0number theory is so cool and interesting to me although my skills suck right now

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0It certainly sounds fun. I'm definitely enjoying my abstract algebra class right now. We had the barest hints of some number theory in discrete math so I'm not completely helpless.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i like these math puzzles

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0differential equations is not as fun to me but i do like the remedial kind lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0zarkon do you think there is hope for my brain?

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0From my experience, I don't like differential equations very much. Granted, I've never had a full course in it, but it just isn't my thing.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i feel like i'm trapped inside with an apes' brain

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0thanks i take that as a compliment

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2If you want a fun class...Take a course in measure theoretic probability theory.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0he says that because he is a stat nerd

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0I don't think my school has that class...

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2or a class in stochastic processes

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2sometimes it will fall under the title of applied probability

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i think they might have that

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i always had a 10 foot pole when it came to statistics i only had to put it down when the course in stat was required

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0I'm personally more of an algebra person. Stats was interesting at first, but then it got boring.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0There are some cool things though in stat i do admit

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2There is plenty of really nice mathematics in statistics

KingGeorge
 4 years ago
Best ResponseYou've already chosen the best response.0It was the same with calculus for me. Interesting at first, and then it just stopped interesting me.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.2A lot of multivariate calculus and matrix theory

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0zarkon can i ask another question

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0this is my last problem with this proof...

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0omg never i got it lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0i was typing it all out then i realized oh yeah lol

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0ok i feel good about this proof thanks for all your help
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